A characterization of Cauchy kernels.
A discrete Hardy-Laptev-Weidl-type inequality and associated Schrödinger-type operators.
A Laplace-like method for solving linear difference equations.
A new approach to the problem of constructing recurrence relations for the Jacobi coefficients
A note on a general difference-functional equation.
A solution to a problem of J. Schwaiger.
A study of resolvent set for a class of band operators with matrix elements
For operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior of the corresponding systems of vector orthogonal polynomials on the resolvent set. We also find that the operators generated by infinite Jacobi matrices have the largest resolvent set in this class.
A symbolic operator approach to power series transformation-expansion formulas.
A unified class of polynomials.
Almost localization and almost reducibility
An extremal problem related to probability.
An inverse problem for the discrete periodic Schrödinger operator.
An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations
We establish an optimal, linear rate of convergence for the stochastic homogenization of discrete linear elliptic equations. We consider the model problem of independent and identically distributed coefficients on a discretized unit torus. We show that the difference between the solution to the random problem on the discretized torus and the first two terms of the two-scale asymptotic expansion has the same scaling as in the periodic case. In particular the L2-norm in probability of the H1-norm...
Bethe ansatz solutions to quasi exactly solvable difference equations.
Chain sequences and compact perturbations of orthogonal polynomials.
Characterization of functions whose forward differences are exponential polynomials
Given a finite subset of , we study the continuous complex valued functions and the Schwartz complex valued distributions defined on with the property that the forward differences are (in distributional sense) continuous exponential polynomials for some natural numbers .
Characterizing polynomials by forward differences.
Classification rationnelle et confluence des systèmes aux différences singuliers réguliers
En choisissant des “caractères” et des “logarithmes”, méromorphes sur , construits à l’aide de la fonction Gamma d’Euler, et en utilisant des séries de factorielles convergentes, nous sommes en mesure, dans une première partie, de donner une “forme normale” pour les solutions d’un système aux différences singulier régulier. Nous pouvons alors définir une matrice de connexion d’un tel système. Nous étudions ensuite, suivant une idée de G.D. Birkhoff, le lien de celles-ci avec le problème de la classification...
Commuting difference operators with polynomial eigenfunctions
Criterion of -criticality for one term -order difference operators
We investigate the criticality of the one term -order difference operators . We explicitly determine the recessive and the dominant system of solutions of the equation . Using their structure we prove a criticality criterion.